FTL

题意翻译

有两艘飞船，第 $i$ 艘飞船（$i∈[1,2]$）的攻击力为 $p_i$，每一次攻击的充能时间为 $t_i$，一开始两艘飞船没有充能。 现在要打败敌方飞船，敌方飞船的血量为 $h$，防御力为 $s$。对于一次攻击力为 $P$ 的攻击，敌方飞船的血量会减少 $(P-s)$。每一次攻击可以是一艘飞船单独攻击，也可以是两艘飞船同时攻击（当一艘飞船完成充能后，可以等待另一艘飞船充能，然后再一起攻击）。两艘飞船一起攻击的攻击力为 $p_1+p_2$。 打败敌方飞船的条件是使得敌方飞船的血量小于等于 $0$。现在依次给出 $p_1,t_1,p_2,t_2,h,s$，求出最少需要多少时间能够打败敌方飞船。

题目描述

Monocarp is playing a video game. In the game, he controls a spaceship and has to destroy an enemy spaceship. Monocarp has two lasers installed on his spaceship. Both lasers $ 1 $ and $ 2 $ have two values: - $ p_i $ — the power of the laser; - $ t_i $ — the reload time of the laser. When a laser is fully charged, Monocarp can either shoot it or wait for the other laser to charge and shoot both of them at the same time. An enemy spaceship has $ h $ durability and $ s $ shield capacity. When Monocarp shoots an enemy spaceship, it receives $ (P - s) $ damage (i. e. $ (P - s) $ gets subtracted from its durability), where $ P $ is the total power of the lasers that Monocarp shoots (i. e. $ p_i $ if he only shoots laser $ i $ and $ p_1 + p_2 $ if he shoots both lasers at the same time). An enemy spaceship is considered destroyed when its durability becomes $ 0 $ or lower. Initially, both lasers are zero charged. What's the lowest amount of time it can take Monocarp to destroy an enemy spaceship?

输入输出格式

输入格式

The first line contains two integers $ p_1 $ and $ t_1 $ ( $ 2 \le p_1 \le 5000 $ ; $ 1 \le t_1 \le 10^{12} $ ) — the power and the reload time of the first laser. The second line contains two integers $ p_2 $ and $ t_2 $ ( $ 2 \le p_2 \le 5000 $ ; $ 1 \le t_2 \le 10^{12} $ ) — the power and the reload time of the second laser. The third line contains two integers $ h $ and $ s $ ( $ 1 \le h \le 5000 $ ; $ 1 \le s < \min(p_1, p_2) $ ) — the durability and the shield capacity of an enemy spaceship. Note that the last constraint implies that Monocarp will always be able to destroy an enemy spaceship.

输出格式

Print a single integer — the lowest amount of time it can take Monocarp to destroy an enemy spaceship.

输入输出样例

输入样例 #1

5 10
4 9
16 1

输出样例 #1

20

输入样例 #2

10 1
5000 100000
25 9

输出样例 #2

25

说明

In the first example, Monocarp waits for both lasers to charge, then shoots both lasers at $ 10 $ , they deal $ (5 + 4 - 1) = 8 $ damage. Then he waits again and shoots lasers at $ 20 $ , dealing $ 8 $ more damage. In the second example, Monocarp doesn't wait for the second laser to charge. He just shoots the first laser $ 25 $ times, dealing $ (10 - 9) = 1 $ damage each time.

题意翻译

有两艘飞船，第 $i$ 艘飞船（$i∈[1,2]$）的攻击力为 $p_i$，每一次攻击的充能时间为 $t_i$，一开始两艘飞船没有充能。 现在要打败敌方飞船，敌方飞船的血量为 $h$，防御力为 $s$。对于一次攻击力为 $P$ 的攻击，敌方飞船的血量会减少 $(P-s)$。每一次攻击可以是一艘飞船单独攻击，也可以是两艘飞船同时攻击（当一艘飞船完成充能后，可以等待另一艘飞船充能，然后再一起攻击）。两艘飞船一起攻击的攻击力为 $p_1+p_2$。 打败敌方飞船的条件是使得敌方飞船的血量小于等于 $0$。现在依次给出 $p_1,t_1,p_2,t_2,h,s$，求出最少需要多少时间能够打败敌方飞船。